Volume 7, issue 2 (2003)

Download this article
For printing
Recent Issues

Volume 27
Issue 9, 3387–3831
Issue 8, 2937–3385
Issue 7, 2497–2936
Issue 6, 2049–2496
Issue 5, 1657–2048
Issue 4, 1273–1655
Issue 3, 823–1272
Issue 2, 417–821
Issue 1, 1–415

Volume 26, 8 issues

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Interests
Editorial Procedure
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Author Index
To Appear
 
Other MSP Journals
Equivariant Euler characteristics and $K$–homology Euler classes for proper cocompact $G$–manifolds

Wolfgang Lueck and Jonathan Rosenberg

Geometry & Topology 7 (2003) 569–613
Bibliography
1 H Abels, A universal proper $G$–space, Math. Z. 159 (1978) 143 MR0501039
2 M F Atiyah, I M Singer, The index of elliptic operators III, Ann. of Math. $(2)$ 87 (1968) 546 MR0236952
3 S Baaj, P Julg, Théorie bivariante de Kasparov et opérateurs non bornés dans les $C^{*}$–modules hilbertiens, C. R. Acad. Sci. Paris Sér. I Math. 296 (1983) 875 MR715325
4 B Blackadar, $K$–theory for operator algebras, Mathematical Sciences Research Institute Publications 5, Springer (1986) MR859867
5 J F Davis, W Lück, Spaces over a category and assembly maps in isomorphism conjectures in $K$– and $L$–theory, $K$–Theory 15 (1998) 201 MR1659969
6 T tom Dieck, Transformation groups, de Gruyter Studies in Mathematics 8, Walter de Gruyter & Co. (1987) MR889050
7 J Dixmier, $C^*$–algebras, North-Holland Mathematical Library 15, North-Holland Publishing Co. (1977) MR0458185
8 M P Gaffney, A special Stokes's theorem for complete Riemannian manifolds, Ann. of Math. $(2)$ 60 (1954) 140 MR0062490
9 N Higson, A primer on $KK$–theory, from: "Operator theory: operator algebras and applications, Part 1 (Durham, NH, 1988)", Proc. Sympos. Pure Math. 51, Amer. Math. Soc. (1990) 239 MR1077390
10 D S Kahn, J Kaminker, C Schochet, Generalized homology theories on compact metric spaces, Michigan Math. J. 24 (1977) 203 MR0474274
11 J Kaminker, J G Miller, Homotopy invariance of the analytic index of signature operators over $C^{*}$–algebras, J. Operator Theory 14 (1985) 113 MR789380
12 G G Kasparov, The operator $K$–functor and extensions of $C^{*}$–algebras, Izv. Akad. Nauk SSSR Ser. Mat. 44 (1980) 571, 719 MR582160
13 G G Kasparov, Equivariant $KK$–theory and the Novikov conjecture, Invent. Math. 91 (1988) 147 MR918241
14 T Kato, Perturbation theory for linear operators, Classics in Mathematics, Springer (1995) MR1335452
15 H B Lawson Jr., M L Michelsohn, Spin geometry, Princeton Mathematical Series 38, Princeton University Press (1989) MR1031992
16 W Lück, Transformation groups and algebraic $K$–theory, Lecture Notes in Mathematics 1408, Springer (1989) MR1027600
17 W Lück, $L^2$–invariants: theory and applications to geometry and $K$–theory, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) 44, Springer (2002) MR1926649
18 W Lück, Chern characters for proper equivariant homology theories and applications to $K$– and $L$–theory, J. Reine Angew. Math. 543 (2002) 193 MR1887884
19 W Lück, The relation between the Baum–Connes conjecture and the trace conjecture, Invent. Math. 149 (2002) 123 MR1914619
20 W Lück, J Rosenberg, The equivariant Lefschetz fixed point theorem for proper cocompact $G$–manifolds, from: "High-dimensional manifold topology", World Sci. Publ., River Edge, NJ (2003) 322 MR2048727
21 D Meintrup, On the type of the universal space for a family of subgroups, PhD thesis, Universität Münster (2000)
22 J Rosenberg, Analytic Novikov for topologists, from: "Novikov conjectures, index theorems and rigidity, Vol. 1 (Oberwolfach, 1993)", London Math. Soc. Lecture Note Ser. 226, Cambridge Univ. Press (1995) 338 MR1388305
23 J Rosenberg, The $K$–homology class of the Euler characteristic operator is trivial, Proc. Amer. Math. Soc. 127 (1999) 3467 MR1610789
24 J Rosenberg, The $G$–signature theorem revisited, from: "Tel Aviv Topology Conference: Rothenberg Festschrift (1998)", Contemp. Math. 231, Amer. Math. Soc. (1999) 251 MR1707347
25 J Rosenberg, The $K$–homology class of the equivariant Euler characteristic operator, unpublished preprint
26 J Rosenberg, S Weinberger, Higher $G$–signatures for Lipschitz manifolds, $K$–Theory 7 (1993) 101 MR1235284
27 J Rosenberg, S Weinberger, The signature operator at 2, Topology 45 (2006) 47 MR2170494
28 J P Serre, Linear representations of finite groups, Graduate Texts in Mathematics 42, Springer (1977) MR0450380
29 S Waner, Y Wu, The local structure of tangent $G$–vector fields, Topology Appl. 23 (1986) 129 MR855452
30 S Waner, Y Wu, Equivariant $\mathrm{SKK}$ and vector field bordism, Topology Appl. 28 (1988) 29 MR927280